Final Fantasy XIV- The Nightmare, Elemental Ponies, Lanners Lore
The first thing to remember with items like these is that the lore train runs both tracks; sometimes content is designed to reflect the lore, sometimes lore is designed to reflect the content. It's literally a chicken and egg situation in terms of development. Thus, it's probable (though not explicitly confirmed) that we were getting ponies and birbs regardless and the lore team was told to make it work, so don't be too disappointed if it turns out that the roots don't run all that deep.
I may be mistaken, but I think the majority of the lore is just based on a pun. A mare can be either a female horse or an evil spirit / demon from Germanic folklore that sits on your chest and gives you bad dreams (likely inspired by sleep paralysis), which gave rise to the term "nightmare". The mount is both a dark horse and an evil spirit, and thus a nightmare forsooth.
Given that the Ascians were handing them out like candy, I imagine they're some kind of void unicorn, yes? Black coat, glowing eyes, etc. It's horn has a flame aura and its feet have both earth and wind auras, which are probably more based in the three primals that the mount drops from than anything else. So I suppose we take it at everyone's word that the nightmares are "manifest darkness".
These are (allegedly) simply Nightmares given to the beast tribes by the Ascians, which were in turn immediately sacrificed to their respective gods and reborn from the void re-cast by elemental aspect. Is there more to it? Perhaps. Is it just technobabble for a gimmick mount dressed up in something vaguely along the lines of what we've seen from primals in the past? Possibly. (EDIT: Sans Boreas, which was a regular unicorn.)
Going by the descriptions of the Round Lanner, it seems that these great falcons are pretty common in the Dravanian and Abalathian skies. In all of the cases so far, it seems the lanners took on auras by either gaining an entity's "favor" by either being mounts of prestiege or just happening to roost in a relevant location (such as the Dark Lanner, which roosted in the Aery and became corrupted by malice).
I find it interesting that the Warring Lanner refers to Sephirot as a primal.
So long as we're meant to be questioning just how different they are, shouldn't that say ... eikon?